Wireless keyboard A1016: fading connection

My keyboard works OK, so long as I keep using it. But if I leave for more than an hour or two, on restarting work, it behaves bizarrely:

• Some keys do not respond

• Others keep sending - a continuous stream of the same character

• Others throw up a tab on screen with all the options [Umlauts, diacriticals, obscure Nordic phonemes etc.]

I have to switch it off. Then, after between 5 and 60 seconds, the screen responds "Disconnected". Then switch it back on, and after between 5 and 300 seconds, the screen responds "Connected".

And all is well. Until the next time I leave it . . . .

What is happening? And how can I cure it?